Allowing for the back effects of an in-stream turbine array deployed in a limited region of a larger scale flow was discussed in Chapter 2. As noted, a theoretical study by Garrett and Cummins (2013) examined the maximum power that could be obtained from an array of turbines in an otherwise uniform region without lateral boundaries. The study assumes water of constant depth, with the turbines effectively assumed to occupy the whole vertical water column so that the flow is modeled as two-dimensional (horizontal variations only). The effect of the turbines is represented as a drag in addition to any natural friction. As the additional drag is increased, the power also increases at first, but the currents inside the circle decrease as the flow is diverted and, as in other situations, there is a point at which the extracted power starts to decrease. The maximum power obtainable from the turbine array depends strongly on the local flow. In most instances, the power from the array of turbines will be limited to a fraction of the kinetic energy flux impinging on the turbine array, most likely no more than approximately 0.7 times the incident flux. If, however, the array is very large (for example, hundreds of square kilometers), the theoretical power could be limited by friction and would be between 50 and 75 percent11 of the natural frictional dissipation of the undisturbed flow in the region containing the turbines (Garrett and Cummins, 2013).
In other words, more than a fraction of the incident energy flux can be obtained only for very large arrays, and then it scales with the natural dissipation in the region. The technical resource will be less than the theoretical resource, possibly considerably less, because of factors that include wake losses and drag on supporting structures. Furthermore, this estimate does not allow for a reduction of the incident flow due to the impact of a large turbine farm on the larger-scale regional flow. High-resolution numerical modeling of disturbed flow due to MHK array deployment would provide a fundamental theoretical foundation for optimizing turbine locations. An optimal layout would locate turbines outside the wake of upstream turbines, while minimizing the distance between devices to lower cable costs. Because these types of optimizations are site-specific, it would be useful to model the most favorable layout for the Florida Current to provide a better estimate of the available technical resource.
The committee further considered the global potential of ocean currents. While there is 800 GW of global dissipation by steady currents, 80 percent of that occurs in the Southern Ocean. B. Polagye and M. Kawase of the University of Washington (personal communication, 2011) apportion the rest by area, assigning only 20 GW to the North Atlantic.
11 The fraction is 0.5 if the friction is taken to be linear in the local current speed and 0.75 if it is taken to be quadratic.